Dynamical Compensation for AC Stark Shift During Kerr-Cat Qubit Initial-State Preparation

A Kerr-cat qubit can be realized by applying a two-photon drive to a nonlinear resonator with small Kerr. However, such a drive shifts the frequency of the qubit, which is known as the a.c. Stark shift. Furthermore, during the ramping up process the a.c. Stark shift is dynamically increased as a function of the drive amplitude. If not compensated correctly, this a.c. Start shift will lead to high-level excitation of the Kerr-cat qubit, resulting in quantum information leakage. In this work, we provide a dynamic compensation method to improve the fidelity of the initial-state preparation of Kerr-cat qubit by slowly changing the drive frequency to dynamically ensure that at each moment the a.c. Stark shift is properly compensated. We show the significant difference between cases with and without the dynamic compensation method when the a.c. Stark shift is large. This work provides a potential approach for preparing large cat qubit and can be extended to other cat qubit operations.